Brief Chronicles V (2014) 113 Bayesian Interrogation of the Elizabethan Social Network for First Folio Authorship Stuart Nettleton lizabeth I’s court favorites and heroes such as Robert Dudley, Walter Raleigh, Francis Drake, and enigmatic polymaths like Francis Bacon and John Dee Eprovided fertile ground for the English Renaissance. Such was the demand for new entertainment in this exciting era that around 2,400 plays were presented from 1590-1642.1 Of these, about two per cent were the Shakespearian canon. A playwright’s intellectual property was generally protected through registration and censorship approval. However, plays usually had little economic value after the typical performance period of one week. While William Shakespeare may be a notable exception, the vocation of playwright was a hand to mouth existence and often dependent upon the favor of a wealthy patron. A number of Medici-like patron-families economically sponsored and shepherded players groups. Foremost among them were Robert and Ambrose Dudley, the patrons respectively of Leicester’s Men and Warwick’s Men. The Stanley family was an early patron of the Lord Admiral’s Men and Lord Strange’s Men (or Derby’s Men), which probably became the Herbert family’s Pembroke’s Men. Similarly, the de Vere family sponsored a boy troupe, the Oxford’s Men and later adopted the Warwick’s Men. Royal approval ensued with Elizabeth I’s patronage of the Queens’ Men, which drew on Robert Dudley’s Leicester’s Men, and the company with whom William Shakespeare associated, the Lord Chamberlain’s Men, evolving into the King’s Men under James I’s patronage. Official documents, private letters, insightful commentaries and gossips record Elizabethan social relationships in considerable detail. One of relatively few thin patches in this social fabric is the Shakespeare authorship question. Prima facie evidence for William Shakespeare’s authorship is indisputable, with that name being Nettleton- Bayesian Interrogation 114 recorded on the latter two-thirds of Shakespearean plays and in the First Folio. The surfeit of such records rests somewhat incongruously alongside a dearth of independent documentary evidence. This issue may be of little consequence to many persons, but others feel challenged by the mystery of this inconsistency or seek to better appreciate Western culture through developing an improved understanding of Shakespeare’s depth of character. The latter group believes that it is a moral imperative to discover whether the dazzling and multidimensional playwright “Shakespeare” was someone other than the sharp businessman, lender and grain hoarder from Stratford-on-Avon portrayed in the few extant legal records. In recent decades this controversial topic has grown in both intrigue and scope. Over sixty candidates have been put forward for potential authorship and the presentation of arguments is becoming ever more flamboyant. For example, a number of U.S. Supreme Court Justices have expressed opinions about the candidacy of Edward de Vere, 17th Earl of Oxford. At a 1987 moot court, three Justices ruled in favorfavour of the Stratford man. But by 2009 three of Justices favored Oxford’s authorship, two favoured William Shakspere of Stratford and four abstained. Edward de Vere’s candidacy remains very much alive. A recent feature film, Anonymous, with a production cost of $27.5 million, controversially argued his case.2 The potential authors selected for study are: William Shakspere of Stratford- on-Avon (1554-1616), Edward de Vere, 17th Earl of Oxford (1550-1604), Christopher Marlowe (1564–1593), Francis Bacon, 1st Viscount St. Albans (1561–1626), Mary Sidney, Countess of Pembroke (1561-1621), Sir Philip Sidney, brother of Mary Sidney (1554–1586), Roger Manners, 5th Earl of Rutland (1576-1612), William Stanley, 6th Earl of Derby (1561-1642), Edward Dyer (1543-1607), Elizabeth I (1533–1603) and Mary Sidney’s niece Mary Wroth (1587-1651/3). Mary Wroth is included since she was a renowned poet and author of the first known piece of fiction in the English language. Born in 1587, she would have been only eleven years old when the first plays were printed. Nevertheless, she would be of interest if she contributed to the later plays as part of an authorship group. The wealth of extant information on Elizabethan social relationships provides a framework amenable to social network analysis. While researchers routinely highlight particular social relationships as ad hoc elements in their historical and literature research, formal mathematical social network analysis using random exponential graph models (ERGM) has not hitherto been applied to a more dynamic understanding of important relationships in the Elizabethan theater. The first part of this research applies new Bayesian ERGM techniques to investigate these eleven authors against the background of the wider Elizabethan Social Network. Over the last five years ERGM techniques have matured using Markov Chain Monte Carlo integration, maximum likelihood estimation and shared partner statistics that address potential model degeneracy.3 The second part applies modern cryptography with log likelihood estimators to a cipher that may increase the authorship probability of Mary Sidney, Countess of Pembroke, who is a prime candidate. The seat of the Earls of Pembroke at Wilton House, near Salisbury, has been a cultural icon for many centuries. Kennedy writes, Brief Chronicles V (2014) 115 “The Earls of Pembroke had from the reign of Henry VIII been encouragers of fine arts, and very early shewed their taste in employing Holbein and Jones in improving their noble seat at Wilton.”4 In 1743 Henry Herbert (c.1689-1750), 9th Earl of Pembroke, commissioned Peter Sheemakers to sculpt a statue of William Shakespeare for Wilton House. It was placed in the Black Marble Table Room alongside an ancient bust purchased by his father, Thomas Herbert (1656-1733), th8 Earl of Pembroke, “The Bustos of LYSIAS the Orator, of whom Cicero gives this Commendation: Venustissimus scriptor ac politissimus, & alter pene Demosthenes.”5 The Wilton Shakespeare statue is almost identical to one in Westminster Abbey, also by Peter Sheemakers. Aside from their bases, the only difference between the statues is the verse inscribed on the scroll held by the statue: Scroll in Wilton House Scroll in Westminster Abbey (from Macbeth 5.5.24-6) (modified from The Tempest 4.1) LIFE’s but a walking SHADOW The Cloud cupt Tow’rs, a poor PLAYER The Gorgeous Palaces That struts and frets his hour upon the The Solemn Temples, STAGE, The Great Globe itself And then is heard no more! Yea all which it Inherit, Shall Dissolue; And like the baseless Fabrick of a Vision Leave not a wreck behind. Table 1: Shakespeare Scroll Inscriptions at Wilton House and Westminster Abbey. In Westminster Abbey, Shakespeare’s finger points to the capitalized word “Temples,” whereas at Wilton House the it points to the all upper case word “SHADOW.” It may be preemptory to conclude that the word “SHADOW” means that William Shakspere was merely a shadow of the real author. The interpretation that Shakspere was a shadow player does not make sense because he was a real player. Perhaps there is some sense to be made of these words if the order is shifted to “shadow life stage player” since Shakspere is thought to have played parts such as Banquo’s ghost. However, it seems unlikely that this would warrant special mention on the statue. In times past it was considered intellectually piquant to place ciphers in full view, often as capital or italic letters within normal text. If this is the case then a full cipher problem may exist as “LIFE SHADOW PLAYER STAGE”. While this cipher appeared over a century after her death, Mary Sidney was deeply engaged in code, secret inks and advanced metaphysics of the day. For example, Walter Raleigh’s half- brother Adrian Gilbert maintained an alchemist’s laboratory at Wilton House.6 While a feasible solution to a cipher cannot be regarded as evidence, modern techniques that determine result log likelihoods can rank solutions in confidence. If Nettleton- Bayesian Interrogation 116 a solution is found it may be possible to incorporate this extra information into an improved Bayesian posterior probability for an authorship candidate. For example, if a cipher solution has a useful probability and the cipher credibly refers to Mary Sidney, then Bayes Rule may be used to calculate a significantly improved posterior probability for her authorship. Methodology The methodology of this research has two parts. The first part is a Bayesian estimation of authorship probabilities for each potential author based on ERGM analysis of the Elizabethan Social Network. The second phase of the research applies Bayesian methods to investigate an improvement in the probability of Mary Sidney’s authorship given the log likelihood of a cryptographic solution to the Wilton House cipher. 1.1. ERGM Research Methodology The general form of the ERGM model was first proposed by Frank & Strauss in 1986.7 Pairing, or dyad relationships, develop between two people (or nodes) based on the attractiveness of the attributes of each to the other. Triad relationships are triangles involving three people. Classic triad closure occurs when two nodes that have independent dyad relationships to a common node, form a relationship and thereby create a triangle.8 Stochastic transitivity is the process of increasing the number of triads through of evolving friendships, i.e., “the friends of my friends become my friends.” This matches real dynamic social networks, in practice, which display a propensity for triad closure. ERGM probabilistic models for the observed network of relationships are evaluated using logistic regression. A key advantage of the ERGM approach is that the restrictive assumption of dyadic independence may be relaxed in favor of stochastic transitivity. ERGM achieves this through a Geometrically Weighted Edge Shared Partner (GWESP) factor. This associates a higher probability with networks that have a greater density of triads.